Calculus of Variations and Geometric Measure Theory
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L. Ambrosio - J. Bertrand

DC Calculus

created by ambrosio on 13 May 2015

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Submitted Paper

Inserted: 13 may 2015
Last Updated: 13 may 2015

Year: 2015

Abstract:

In this paper, we extend the DC Calculus introduced by Perelman on finite dimensional Alexandrov spaces with curvature bounded below. Among other things, our results allow us to define the Hessian and the Laplacian of DC functions (including distance functions as a particular instance) as a measure-valued tensor and a Radon measure respectively. We show that these objects share various properties with their analogues on smooth Riemannian manifolds.

Tags: GeMeThNES


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